Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Gromov's Oka principle for equivariant maps (1912.07129v2)

Published 15 Dec 2019 in math.CV, math.AG, and math.RT

Abstract: We take the first step in the development of an equivariant version of modern, Gromov-style Oka theory. We define equivariant versions of the standard Oka property, ellipticity, and homotopy Runge property of complex manifolds, show that they satisfy all the expected basic properties, and present examples. Our main theorem is an equivariant Oka principle saying that if a finite group $G$ acts on a Stein manifold $X$ and another manifold $Y$ in such a way that $Y$ is $G$-Oka, then every $G$-equivariant continuous map $X\to Y$ can be deformed, through such maps, to a $G$-equivariant holomorphic map. Approximation on a $G$-invariant holomorphically convex compact subset of $X$ and jet interpolation along a $G$-invariant subvariety of $X$ can be built into the theorem. We conjecture that the theorem holds for actions of arbitrary reductive complex Lie groups and prove partial results to this effect.

Summary

We haven't generated a summary for this paper yet.